Wyman, the son of a commercial fisherman and a typist, grew up in Kearny, New Jersey, where he worked in the factories during summers to pay for college. He acquired an appreciation for the "no-nonsense functional aesthetic of the sea and the factories", which he has described as "an important influence in my approach to design." He graduated from the Pratt Institute with a degree in industrial design in 1960. The subject of graphic design was just being introduced in American universities at the time; when Wyman met a student who studied logo design with Paul Rand at Yale, he wanted to design logos.
Wyman began his career in Detroit, Michigan, at General Motors, where he worked on a packaging system for Delco automotive parts that unified 1,200 different packages. Later, he moved to the office of William Schmidt, where he produced the graphics for the American pavilion at a 1962 trade fair in Zagreb, Yugoslavia.
In 1963, Wyman moved to New York, where he joined the George Nelson firm. He designed the graphics for the Chrysler Pavilion at the New York World's Fair. He later reported that devising a "pointing hand" theme logo and adapting it to the site directional signs convinced him that logos could play a more important role in an overall design program. In 1966, he participated in a design competition for the graphics for the 1968 Mexico Olympic Games. His "Mexico68" logotype was the winner, and launched his career. Wyman remained in Mexico for four and one-half years, following his Olympic work with development of graphic programs for the Mexico City Metro and the 1970 World Cup competition.
After returning to New York in 1971, Wyman formed a partnership with Bill Cannan (Wyman & Cannan). In 1979, he established his own firm, Lance Wyman Ltd. He has also taught corporate and wayfinding design at Parsons School of Design since 1973.
Wyman, who has been described as a "rock star" of graphic arts, made his reputation when he collaborated with Eduardo Terrazas, under the direction of Architect Ramirez Vazquez, in the development of the entire design campaign for the Mexico 1968 Summer Olympic Games. He has also designed icons for museums and many other institutions, individualized signs for buildings at the National Zoo in Washington D.C., and many other symbols. Stepping outside his usual genre, he designed a poster for the 2008 Barack Obama presidential campaign. Perhaps his most enduring design is the stylized route map he devised for the Washington Metro in the mid-1970s, showing routes, stations, transfer points, and certain landmarks in a clear fashion, although distances are not to scale. In 2011, Wyman was called on to design a new Metro map, able to depict planned new lines and route orientations, as well as some station names that have been expanded to the point of being cumbersome. It is one of the few occasions in which the original designer has a chance to revise his own creation. The new map debuted March 19, 2012, and an update was announced on September 12, 2013.